This page is intended as a brief overview of delimited continuations and related constructs, and how they can be used in Haskell. It uses the library CC-delcont as a vehicle for doing so, but the examples should be general enough so that if you have another implementation, they should be relatively straight forward to port (whenever possible, I have endeavored not to use the operators on abstract prompt and sub-continuation types from CC-delcont, instead using the more typical, functional operators).

This page is intended as a brief overview of delimited continuations and related constructs, and how they can be used in Haskell. It uses the library CC-delcont as a vehicle for doing so, but the examples should be general enough so that if you have another implementation, they should be relatively straight forward to port (whenever possible, I have endeavored not to use the operators on abstract prompt and sub-continuation types from CC-delcont, instead using the more typical, functional operators).

+

+

== The Basics ==

+

+

=== Undelimited Continuations ===

+

+

If you've taken university courses in computer science, or done much investigation of language design, you've probably encountered continuations before. The author first recalls learning about them in a class on said subject, where they were covered very briefly, and it was mentioned (without proof; and no proof will be provided here) that they could be used as a basis upon which all control flow operators could be built. At the time, they seemed rather abstract and unwieldy. Perhaps they could be used to implement any more common control flow pattern, but why bother, when, as far as language implementation concerns go, it's easier to implement (and understand) most common control flow directly than it is to implement continuations?

+

+

As far as usage goes, continuations are probably most closely associated with Scheme, and its call-with-current-continuation function (abbreviated to Haskell's version, callCC from now on), although many other languages have them (undelimited continuations for Haskell are provided by the Cont monad and ContT transformer). They're often regarded as being difficult to understand, as their use can cause very complex control flow patterns (much like GOTO, although more sophisticated), though reduced to their basics, they aren't that hard to understand.

+

+

A continuation of an expression is, in a loose sense, 'the stuff that happens after the expression.' An example to refer to may help:

+

+

m >>= f >>= g >>= h

+

+

Here we have an ordinary monadic pipeline. A computation m is run, and its result is fed into f, and so on. We might ask what the continuation of 'm' is, the portion of the program that executes after m, and it looks something like:

+

+

\x -> f x >>= g >>= h

+

+

The continuation takes the value produced by m, and feeds it into 'the rest of the program.' But, the fact that we can represent this using functions as above should be a clue that continuations can be built up using them, and indeed, this is the case. There is a standard way to transform a program written normally (or in a monadic style, as above) into a program in which continuations, represented as functions, are passed around explicitly (known as the CPS transform), and this is what Cont/ContT does.

+

+

However, such a transform would be of little use if the passed continuations were inaccessible (as with any monad), and callCC is just the operator for the job. It will call a function with the implicitly passed continuation, so in:

+

+

callCC (\k -> e) >>= f >>= g >>= h

+

+

'k' will be set to a function that is something like the above '\x -> f x >>= g >>= h'. However, in some sense, it is not an ordinary function, as it will never return to the point where it is invoked. Instead, calling 'k' should be viewed as execution jumping to the point where callCC was invoked, with the entire 'callCC (..)' expression replaced with the value passed to 'k'. So k is not merely a normal function, but a way of feeding a value into into an execution context (and this is reflected in its monadic type: a -> Cont b).

+

+

So, what is all this good for? Well, a standard example is that one can use continuations to capture a method of escaping from loops (particularly nested ones), and if you ponder for a while, you might be able to imagine implementing some sort of exception mechanism with them. A simple example is computing the product of a list of numbers:

+

+

<haskell>

+

prod l = callCC (\k -> loop k l)

+

where

+

loop _ [] = return 1

+

loop k (0:_) = k 0

+

look k (x:xs) = do n <- loop k xs ; return (n*x)

+

</haskell>

+

+

Under normal circumstances, the loop will simply multiply all the numbers. However, if a 0 is detected, there is no need to multiply anything, the answer will always be 0. So, the continuation is invoked, and 0 is returned immediately, without performing any multiplications.

== CC-delcont ==

== CC-delcont ==

Revision as of 06:38, 17 July 2007

Contents

1 Introduction

This page is intended as a brief overview of delimited continuations and related constructs, and how they can be used in Haskell. It uses the library CC-delcont as a vehicle for doing so, but the examples should be general enough so that if you have another implementation, they should be relatively straight forward to port (whenever possible, I have endeavored not to use the operators on abstract prompt and sub-continuation types from CC-delcont, instead using the more typical, functional operators).

2 The Basics

2.1 Undelimited Continuations

If you've taken university courses in computer science, or done much investigation of language design, you've probably encountered continuations before. The author first recalls learning about them in a class on said subject, where they were covered very briefly, and it was mentioned (without proof; and no proof will be provided here) that they could be used as a basis upon which all control flow operators could be built. At the time, they seemed rather abstract and unwieldy. Perhaps they could be used to implement any more common control flow pattern, but why bother, when, as far as language implementation concerns go, it's easier to implement (and understand) most common control flow directly than it is to implement continuations?

As far as usage goes, continuations are probably most closely associated with Scheme, and its call-with-current-continuation function (abbreviated to Haskell's version, callCC from now on), although many other languages have them (undelimited continuations for Haskell are provided by the Cont monad and ContT transformer). They're often regarded as being difficult to understand, as their use can cause very complex control flow patterns (much like GOTO, although more sophisticated), though reduced to their basics, they aren't that hard to understand.

A continuation of an expression is, in a loose sense, 'the stuff that happens after the expression.' An example to refer to may help:

m >>= f >>= g >>= h

Here we have an ordinary monadic pipeline. A computation m is run, and its result is fed into f, and so on. We might ask what the continuation of 'm' is, the portion of the program that executes after m, and it looks something like:

\x -> f x >>= g >>= h

The continuation takes the value produced by m, and feeds it into 'the rest of the program.' But, the fact that we can represent this using functions as above should be a clue that continuations can be built up using them, and indeed, this is the case. There is a standard way to transform a program written normally (or in a monadic style, as above) into a program in which continuations, represented as functions, are passed around explicitly (known as the CPS transform), and this is what Cont/ContT does.

However, such a transform would be of little use if the passed continuations were inaccessible (as with any monad), and callCC is just the operator for the job. It will call a function with the implicitly passed continuation, so in:

callCC (\k -> e) >>= f >>= g >>= h

'k' will be set to a function that is something like the above '\x -> f x >>= g >>= h'. However, in some sense, it is not an ordinary function, as it will never return to the point where it is invoked. Instead, calling 'k' should be viewed as execution jumping to the point where callCC was invoked, with the entire 'callCC (..)' expression replaced with the value passed to 'k'. So k is not merely a normal function, but a way of feeding a value into into an execution context (and this is reflected in its monadic type: a -> Cont b).

So, what is all this good for? Well, a standard example is that one can use continuations to capture a method of escaping from loops (particularly nested ones), and if you ponder for a while, you might be able to imagine implementing some sort of exception mechanism with them. A simple example is computing the product of a list of numbers:

Under normal circumstances, the loop will simply multiply all the numbers. However, if a 0 is detected, there is no need to multiply anything, the answer will always be 0. So, the continuation is invoked, and 0 is returned immediately, without performing any multiplications.

5 More Information

A google search for delimited continuations will likely yield plenty of interesting resources on the subject. However, the following resources proved especially useful to the author when he was investigating them:

Delimited continuations in operating systems -- This paper provides excellent insight into how delimited continuations can arise as a natural solution/model for real problems, specifically in the context of implementing an operating system.

A Monadic Framework for Delimited Continuations -- This is the paper from which the implementation of the above library was derived. It's quite thorough in its explanation of the motivations for the interface, and also has several possible implementations thereof (though CC-delcont uses only one).

Delimited Dynamic Binding -- This paper, and related code, served as the basis for the dynamically scoped variable portion of the CC-delcont library. It explains the rationale for having dynamic scoping and delimited control interact in the way they do in the library, and goes through the implementation of dynamic variables in terms of delimited continuations.

Shift to control -- This paper explores four different sets of delimited control operators (all of which are implemented in CC-delcont), and their implementation. Though it's not directly relevant to this particular library, it provides some good insight into delimited continuations and their implementation in general.

Oleg Kiselyov's continuation page -- Contains plenty of excellent information on delimited continuations and the like (including some of the above papers), including examples of their use in Haskell.